On the Weak Compactness in Banach Lattices

The Grothendieck's criterion of weak compactness in space C(S) has been extended by C.P.Niculescu for weakly sequentially complete Banach lattices. This paper first provides some sufficient and necessary conditions for weakly sequentially complete Banach lattices, with the result that the criterion C.P.Niculescu obtained of the weak compactness has actually characterized the weakly sequentially Banach lattices. At the same time we extend C.P.Niculescu's important results. Then we solve negatively Problem 1.11 which was posed by C.P. Niculescu, and a sufficient condition for this is given which generalizes Pelczynski's result.